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Article Dans Une Revue Discrete Event Dynamic Systems Année : 2013

The level set method for the two-sided max-plus eigenproblem

Résumé

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.

Dates et versions

hal-00940791 , version 1 (02-02-2014)

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Stephane Gaubert, Sergei Sergeev. The level set method for the two-sided max-plus eigenproblem. Discrete Event Dynamic Systems, 2013, 23 (2), pp.105-134. ⟨10.1007/s10626-012-0137-z⟩. ⟨hal-00940791⟩
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